An Etymological Dictionary of the German Language/Annotated/klein – Wikisource, the free online library

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klein, adjective, ‘little,’ from Middle High German klein, kleine, adjective, ‘clean, pretty, fine, prudent, slender, lean, little, insignificant’; Old High German chleini, ‘pretty, shining, neat, careful, slight’ (Alemannian dialects point to an Old High German variant *chlîni). Anglo-Saxon clœ̂ne, adjective, ‘clean, neat,’ English clean, proves that ‘pretty, clean,’ is the primary idea of the various senses of the Middle High German word (compare Schmach). Scandinavian klénn was borrowed at a late period from English, Low German, or Frisian Gothic *klai-ni- is wanting; the nasal belongs, as in several other adjectives. (see rein and schön), to the suffix. It is uncertain whether the root is to be connected with Greek γλαι-όι ‘greasy, sticky oil,’ and its cognates, discussed under Klei (the meanings ‘to shine, cleave (to)’ interchange, e.g., in the root λιπ, Greek λιπα, λίπαρέω, λιπος, λιπαρός). Greek γλήμη, neuter, ‘wonders, ornaments,’ and γλήη, ‘pupil (of the eye),’ are, however, both on account of their forms and meanings, still less allied. —